Breakdown of chiral expansion for parton distributions

TL;DR

This paper shows that standard chiral perturbation theory fails at small x in pion parton distributions, requiring all-order resummation, and provides an example of how to perform this resummation.

Contribution

It demonstrates the breakdown of standard chiral perturbation theory at small x and introduces a resummation method for pion parton distributions.

Findings

Chiral perturbation theory breaks down at small x.

Resummation of all orders is necessary at small x.

Explicit example of resummation provided.

Abstract

In the framework of the chiral perturbation theory we computed two- and three-loop corrections to the pion parton distributions which posses $\delta$-function singularities at x->0. This calculation explicitly demonstrates that in the region of small x ~ mpi^2/(4 pi F)^2 standard ChPT breaks down and one needs resummation of all orders. We give an example of such resummation.